Kerry Back
BUSI 721, Fall 2022
JGSB, Rice University
Daily returns compound to monthly returns, and monthly returns compound to annual returns.
But daily, monthly, and annual return distributions have different properties.
Annual returns are approximately normally distributed, but daily and monthly returns are not.
For normal distributions, skewness = kurtosis = 0.
Higher powers place greater weight on outliers.
Outliers to the left (low) ⇒ negative skewness.
Outliers to the right (high) ⇒ positive skewness.
Outliers ⇒ positive kurtosis.
from pandas_datareader import DataReader as pdr
daily = 'F-F_Research_Data_Factors_daily'
daily = pdr(daily, 'famafrench', 1927)[0]
daily = daily['Mkt-RF'] + daily['RF']
monthly = pdr('F-F_Research_Data_Factors', 'famafrench', 1927)[0]
annual = pdr('F-F_Research_Data_Factors', 'famafrench', 1927)[1]
monthly = monthly['Mkt-RF'] + monthly['RF']
annual = annual['Mkt-RF'] + annual['RF']
print('daily skew and kurt are', daily.skew(), daily.kurt())
print('monthly skew and kurt are', monthly.skew(), monthly.kurt())
print('annual skew and kurt are', annual.skew(), annual.kurt())Results:
(i) skewness is small
(ii) kurtosis is small for annual returns
(iii) kurtosis is high for monthly and very high for daily returns
When were the two best days?
What was the next-to-worst month?